Multicarrier transmission methods are being used increasingly for transmitting information at high transmission rates. Known methods include, for example, the OFDM (orthogonal frequency division multiplexing) transmission method and the DMT (discrete multitone) transmission method. Both methods are based on the implicit synthesis of the multicarrier signal by fast Fourier transformation, and on the use of a cyclic guard interval. This cyclic time interval, which is referred to as a prefix in the specialist world, is inserted between adjacent transmission signal blocks and includes a predetermined number of sample values of a preceding transmission signal block. The use of a prefix allows efficient frequency domain equalization, provided that the impulse response of the equivalent, time-discrete transmission signal is shorter than the length of the prefix. Longer impulse responses require the additional use of a time domain equalizer. A time domain equalizer is applied directly to the sample values of a transmission signal arriving in a receiver. A conventional structure of a receiver and of a transmitter is described, by way of example, in IEEE 1996, pages 56–64, “Optimum Finite-Length Equalization for Multicarrier Transceiver”, Aldhahir. For certain applications—for example for the xDSL transmission technique (x Digital Subscriber Line) or from a technique of transmitting via power supply lines (Power Line Communication),—a bi-directional coordinated setting-up phase is possible, in which an estimated value can be determined for the channel impulse response. This estimated value allows adaptation of the time domain equalizer.
A time domain equalizer in which the coefficients for the time domain equalizer are determined from a channel impulse response with the aid of a substitution system—that is a discrete equalizer model—is already known from the documents IEEE 1995, Van Bladel and Moeneclay; pages 167 to 171, “Time-Domain Equalizer for Multicarrier Communication”. The calculation is carried out as an eigen value problem, which is related to a suitably defined correlation matrix. One disadvantage of this method is that an abstract, mean signal-to-noise ratio is optimized, which does not lead to an optimum rate or to a minimum bit error probability. Such optimization or determination of the filter coefficients is proposed in Henkel and Kessler, “Maximizing the Channel Capacity of Multicarrier Transmission by a Suitable Adaptation Procedure for Time Domain Equalizer”, Deutsche Telekom. This is based on global optimization in a vector space whose dimension is equal to the length of the transversal filter to be adapted, and is typically k=32–64. The unavoidable size of the vector space leads firstly to considerable numerical complexity, that is to say to high computer power, and secondly to instabilities in the optimization procedure, which can lead to a reduction in the achievable data transmission rate.